Dao Gong

On the resonant vibration of a flexible railway car body and its suppression with a dynamic vibration absorber

The geometric filtering phenomenon is first analyzed with a simplified vertical vehicle model. Analytical solutions obtained with this model show that geometric filtering phenomenon consists of ‘wheelbase filtering’ and ‘bogie spacing filtering’ effects. The wheelbase filtering effect occurs when there is neither car body bounce nor pitch response at certain track wavelengths, whereas the bogie spacing filtering effect occurs when there is a null in either the car body bounce or pitch response at particular track wavelengths. Then, the correlated frequency response function for railway vehicles is defined to assess the effect of geometric filtering upon the resonant frequencies of a flexible car body. It is found that if the car body’s first bending frequency coincides with the peak values of bounce acceleration transmissibility, that is, it is near the null pitch response frequencies, resonant vibration of the flexible car body will happen. Finally, to suppress the resonant vibration of the flexible car body, it is proposed to use a dynamic vibration absorber (DVA) suspended under the car body underframe. The DVA parameters are optimized according to car body bending frequency and the null pitch frequency. The optimal DVAs show very good performance and robustness in suppression of the car body resonant vibration.

Vertical random vibration analysis of vehicle--track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Greens function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.

Influence of under-chassis-suspended equipment on high-speed EMU trains and the design of suspension parameters

A numerical method for the calculation of the frequencies of vibration of a car body on a high-speed electric multiple unit train with under-chassis-suspended equipment is proposed. In addition, the design of the parameters of the suspension system for the equipment is presented; it is based on the principles of mode matching, transmissibility matching, and consideration of the optimal vibration of both car body and equipment. It is shown that by tuning the suspension stiffness, the first vertical bending frequency of the car body displays a frequency-hopping phenomenon. The first vertical bending frequency of the car body can be enhanced by optimizing the suspension parameters, so as to suppress the vibrations of both the car body and the suspended equipment.

Analysis of Dynamic Stiffness Effect of Primary Suspension Helical Springs on Railway Vehicle Vibration

Helical springs within the primary suspension are critical components for isolating the whole vehicle system from vibration generated at the wheel/rail contact. As train speeds increase, the frequency region of excitation becomes larger, and a simplified static stiffness can no longer represent the real stiffness property in a vehicle dynamic model. Coil springs in particular exhibit strong internal resonances, which lead to high vibration amplitudes within the spring itself as well as degradation of the vibration isolation. In this paper, the dynamic stiffness matrix method is used to determine the dynamic stiffness of a helical spring from a vehicle primary suspension. Results are confirmed with a finite element analysis. Then the spring dynamic stiffness is included within a vehicle-track coupled dynamic model of a high speed train and the effect of the dynamic stiffening of the spring on the vehicle vibration is investigated. It is shown that, for frequencies above about 50 Hz, the dynamic stiffness of the helical spring changes sharply. Due to this effect, the vibration transmissibility increases considerably which results in poor vibration isolation of the primary suspension. Introducing a rubber layer in series with the coil spring can attenuate this effect.

Analysis of modal frequency optimization of railway vehicle car body

High structural modal frequencies of car body are beneficial as they ensure better vibration control and enhance ride quality of railway vehicles. Modal sensitivity optimization and elastic suspension parameters used in the design of equipment beneath the chassis of the car body are proposed in order to improve the modal frequencies of car bodies under service conditions. Modal sensitivity optimization is based on sensitivity analysis theory which considers the thickness of the body frame at various positions as variables in order to achieve optimization. Equipment suspension design analyzes the influence of suspension parameters on the modal frequencies of the car body through the use of an equipment-car body coupled model. Results indicate that both methods can effectively improve the modal parameters of the car body. Modal sensitivity optimization increases vertical bending frequency from 9.70 to 10.60 Hz, while optimization of elastic suspension parameters increases the vertical bending frequency to 10.51 Hz. The suspension design can be used without alteration to the structure of the car body while ensuring better ride quality.

Study on Vibration Reduction Design of Suspended Equipment of High Speed Railway Vehicles

The design methods of the under-chassis equipment of a high speed railway vehicle based on dynamic vibration absorber (DVA) theory and vibration isolation theory are proposed, respectively. A detailed rigid-flexible coupled dynamic model of a high speed railway vehicle which includes car body flexibility and the excitation of the suspended equipment is established. The vibrations of the car body and the suspension equipment with the proposed design methods are studied. Results show that the elastic vibration of the car body can be decreased effectively by mounting the under-chassis equipment with elastic suspension. Comparing with vibration isolation theory, the method based on DVA theory is more effective for suppressing the car body flexible vibration, but it will increase the vibration of the equipment to a certain extent. The method based on vibration isolation theory can reduce the vibration of both the car body and the equipment at the same time. Therefore, the design method should be selected appropriately according to the specific requirement.

Decoupling Optimization Design of Under-Chassis Equipment Suspension System in High-Speed Trains

The vibrations of high-speed trains may strongly affect the safety and ride comfort of passengers, which issue requires the damping optimization of under-chassis equipment (UCE). In this study, the natural frequency of UCE is determined via the dynamic vibration absorber theory. The performed investigation of UCE-car body system vibration behavior revealed that an eccentricity of UCE results in the coupling vibration in six degrees of freedom, which leads to significant changes in its vibration mode and frequency. Thus, the natural frequency of UCE deviates from the initially determined value, which implies that the vibration damping effect is weakened. In this study, two decoupling optimization design methods, namely, forward and inverse decoupling methods, are proposed to solve this problem. The analysis of results obtained proves the feasibility of the proposed methods, which yield favorable decoupling degrees for the UCE vibration modes and minimize the offset of the vibration mode frequency from the initial natural one. These methods are considered quite instrumental in the improvement of vibration damping effect for high-speed trains.

A New Vibration Absorber Design for Under-Chassis Device of a High-Speed Train

To realize the separation of vertical and lateral stiffness of the under-chassis device, a new type of vibration absorber is designed by using the negative stiffness of the disc spring in parallel with the rubber component. To solve its transmission characteristics, harmonic transfer method was used. A rigid-flexible coupling multibody dynamic model of a high-speed train with an elastic car body is established, and the vertical and lateral optimal stiffness of the under-chassis device are calculated. The Sperling index and acceleration PSD of the vehicle with the new vibration absorber and the vehicle with traditional rubber absorber are compared and analyzed. The results show that, with the new vibration absorber, vehicle’s running stability and vibration of the car body are more effective than the vehicle with the traditional rubber absorber.

Study on Wheel-Rail Coupled Vibration of Metro with Co-Simulation of Finite Element Analysis and Multi-Body Dynamics Simulation

Based on the multi-body dynamics theory and modal-reduction analysis, finite element method and multi-body dynamics were combined to establish the flexible track model. The rigid-flexible coupled dynamics model can reflect the features of coupled vibration accurately. When the flexibility of the rail, damping and stiffness of support layers under the rail are taken into consideration, the whole track structure acted as a buffer while wheel and rail is interacting with each other. Compared with rigid track model, the wheel-rail vibration is less in the flexible track model. The proposed method in this paper is simple and effective, which makes the calculation of vehicle-track dynamic response more convenient and quick.

Analysis of Resonant Vibration of Railway Vehicle

A fully equipped railway vehicle dynamic model which considers the car body flexibility is established to analyze the fundamental reason of car body flexural resonance. Results show that it is the geometric filtering phenomenon rather than the natural vibration of bogie bounce that causes the car body resonant flexural vibration. The higher the vehicle running speed, the higher the first vertical bending frequency should be required.